Answer:
C & D
Step-by-step explanation:
We are given the equation:-
[tex] \displaystyle \large{ {m}^{2} + 144 = 0}[/tex]
Subtract both sides by 144.
[tex] \displaystyle \large{ {m}^{2} + 144 - 144 = 0 - 144} \\ \displaystyle \large{ {m}^{2} = - 144} [/tex]
Square root both sides, adding plus-minus.
[tex] \displaystyle \large{ \sqrt{ {m}^{2} } = \pm\sqrt{ - 144} } \\ \displaystyle \large{ m = \pm\sqrt{ - 144} } [/tex]
Therefore, m is √-144 or - √-144.
Learn More!
These type of number such as √-144 or any negative numbers in square root or nth root where n = (2,4,6,8,...) are called Imaginary Number
Imaginary Number is another set that is separated from Real Number.
When both Real and Imaginary are together, they are called Complex Number
Let's say we want to solve the equation and receive imaginary solutions, let's see the Imaginary Unit.
Imaginary Unit
We usually define 'i' as imaginary unit.
[tex] \displaystyle \large{i = \sqrt{ - 1} } \\ \displaystyle \large{ {i}^{2} = - 1 } \\ \displaystyle \large{ {i}^{3} = - \sqrt{ - 1} = - i} \\ \displaystyle \large{ {i}^{4} = 1}[/tex]
From the equation above:-
[tex] \displaystyle \large{ m = \pm\sqrt{ - 144} } [/tex]
Factor √-1 out of √-144.
[tex] \displaystyle \large{ m = \pm\sqrt{ 144} \sqrt{ - 1} } [/tex]
From the imaginary unit, √-1 = i.
√144 is 12.
Thus:-
[tex] \displaystyle \large{ m = \pm 12i}[/tex]
